James Gregory | |
|---|---|
 Gregory byJohn Scougal,c. 1675 | |
| Born | November 1638 (1638-11) Drumoak,Aberdeenshire, Scotland |
| Died | October 1675(1675-10-00) (aged 36) Edinburgh, Scotland |
| Citizenship | Scotland |
| Alma mater | Marischal College,University of Aberdeen University of Padua |
| Known for | Gregorian telescope Gregory coefficients Diffraction grating Fundamental theorem of the calculus Integral of the secant function |
| Scientific career | |
| Fields | Mathematics Astronomy |
| Institutions | University of St. Andrews University of Edinburgh |
| Notes | |
James GregoryFRS (November 1638 – October 1675) was a Scottish mathematician andastronomer. His surname is sometimes spelt asGregorie, the original Scottish spelling. He described an early practical design for thereflecting telescope – theGregorian telescope – and made advances intrigonometry, discoveringinfinite series representations for several trigonometric functions.
In his bookGeometriae Pars Universalis (1668)[1] Gregory gave both the first published statement and proof of thefundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of the theorem), for which he was acknowledged byIsaac Barrow.[2][3][4][5][6][7][excessive citations]
Gregory was born in 1638. His mother Janet was the daughter ofJean and David Anderson and his father was John Gregory,[8] anEpiscopalianChurch of Scotland minister, James was youngest of their three children and he was born in themanse atDrumoak,Aberdeenshire, and was initially educated at home by his mother, Janet Anderson (~1600–1668). It was his mother who endowed Gregory with his appetite forgeometry, her uncle –Alexander Anderson (1582–1619) – having been a pupil and editor of French mathematicianViète. After his father's death in 1651 his elder brother David took over responsibility for his education. He attendedAberdeen Grammar School, and thenMarischal College from 1653–1657, graduating AM in 1657.
In 1663 he went to London, meetingJohn Collins and fellow ScotRobert Moray, one of the founders of theRoyal Society. In 1664 he departed for theUniversity of Padua, in theVenetian Republic, passing throughFlanders, Paris and Rome on his way. At Padua he lived in the house of his countrymanJames Caddenhead, the professor of philosophy, and he was taught byStefano Angeli. The geometrical treatises he published in Padua,Vera circuli et hyperbolæ quadratura (1667) andGeometriæ pars universalis (1668), testify to the deep influence the works of Angeli and other leading Italian mathematicians, such asGabriele Manfredi, exerted on him.[9]
Upon his return to London in 1668 he was elected aFellow of the Royal Society, before travelling toSt Andrews in late 1668 to take up his post as the firstRegius Professor of Mathematics at theUniversity of St Andrews, a position created for him byCharles II, probably upon the request of Robert Moray. There at theUniversity of St Andrews, he laid the first meridian line across the floor of his lab in 1673, which was 200 years prior to the Greenwich Meridian being established, and thus "arguably making St Andrews the place where time began".[10][11]
He was successively professor at theUniversity of St Andrews and theUniversity of Edinburgh.
He had married Mary, daughter ofGeorge Jameson, painter, and widow of John Burnet of Elrick, Aberdeen; their son James was Professor of Physics atKing's College, Aberdeen. He was the grandfather ofJohn Gregory (FRS 1756); uncle ofDavid Gregorie (FRS 1692) and brother ofDavid Gregory (1627–1720), a physician and inventor.
About a year after assuming the Chair of Mathematics atEdinburgh, James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36.
In theOptica Promota, published in 1663, Gregory described his design for areflecting telescope, the "Gregorian telescope". He also described the method for using thetransit of Venus to measure the distance of the Earth from the Sun, which was later advocated byEdmund Halley and adopted as the basis of the first effective measurement of theAstronomical Unit.
Before he left Padua, Gregory publishedVera Circuli et Hyperbolae Quadratura (1667) in which he approximated the areas of thecircle andhyperbola with convergent series:
"The first proof of thefundamental theorem of calculus and the discovery of theTaylor series can both be attributed to him."[13][14]
The book was reprinted in 1668 with an appendix,Geometriae Pars, in which Gregory explained how the volumes ofsolids of revolution could be determined.
In his 1663Optica Promota, James Gregory described hisreflecting telescope which has come to be known by his name, the Gregorian telescope. Gregory pointed out that a reflecting telescope with aparabolic mirror would correctspherical aberration as well as thechromatic aberration seen inrefracting telescopes. In his design he also placed a concavesecondary mirror with an elliptical surface past the focal point of the parabolicprimary mirror, reflecting the image back through a hole in the primary mirror where it could be conveniently viewed. According to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one.[15]
The telescope design attracted the attention of several people in the scientific establishment such asRobert Hooke, the Oxford physicist who eventually built the telescope 10 years later, and SirRobert Moray,polymath and founding member of theRoyal Society.
The Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications. Gregorian optics are also used inradio telescopes such asArecibo, which features a "Gregorian dome".[16]
The following excerpt is from thePantologia. A new (cabinet) cyclopædia (1813)
Mr. James Gregory was a man of a very acute and penetrating genius. ...The most brilliant part of his character was that of his mathematical genius as an inventor, which was of the first order; as will appear by... his inventions and discoveries [which include] quadrature of the circle and hyperbola, by an infinite converging series; his method for the transformation of curves; a geometrical demonstration ofLord Brouncker's series for squaring the hyperbola—his demonstration that the meridian line is analogous to a scale of logarithmic tangents of the half complements of the latitude; he also invented and demonstrated geometrically, by help of the hyperbola, a very simple converging series for making the logarithms; he sent toMr. Collins the solution of the famousKeplerian problem by an infinite series; he discovered a method of drawingTangents to curves geometrically, without any previous calculations; a rule for the direct and inverse method of tangents, which stands upon the same principle (ofexhaustions) with that offluxions, and differs not much from it in the manner of application; a series for the length of the arc of a circle from the tangent, and vice versa; as also for the secant and logarithmic tangent and secant, and vice versa. These, with others, for measuring the length of the elliptic and hyperbolic curves, were sent to Mr. Collins, in return for some received from him ofNewton's, in which he followed the elegant example of this author, in delivering his series in simple terms, independent of each other.[17]
In a letter of 1671 toJohn Collins, Gregory gives thepower series expansion of the seven functions (using modern notation) (often calledGregory's series), the inverseGudermannian function, and the Gudermannian function[18]
There is evidence that he discovered the method of taking higher derivatives in order to compute a power series, which was not discovered by Taylor until 1715, but did not publish his results, thinking he had only rediscovered "Mr. Newton's universal method," which was based on a different technique.[19]
James Gregory discovered thediffraction grating by passingsunlight through a birdfeather and observing the diffraction pattern produced.[20] In particular he observed the splitting of sunlight into its component colours – this occurred a year after Newton had done the same with aprism and the phenomenon was still highly controversial.
A round wheel is unsuitable for irregular surfaces, and Gregory devised an appropriate "adaptable wheel" using aGregory transformation.[21]
Gregory, an enthusiastic supporter of Newton, later had much friendly correspondence with him and incorporated his ideas into his own teaching, ideas which at that time were controversial and considered quite revolutionary.
The craterGregory on the Moon is named after him. He was the uncle of mathematicianDavid Gregory.
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